Consider the profit function given by f(x, y) = x2 2 x y + y3, where x and y are the quantities of two goods sold by a firm. Suppose that currently the company makes and sells 3 units of the first product, and 2 of the second, and it decides to increase the production (and sales) in the direction v = (2, 3).

(a) Will the profit increase of decrease at the given point p = (3, 2) in the given direction v?

(b) Is the profit function f convex or concave at p in the direction of v?